Multi-phase flow decomposition using electrical capacitance volume tomography sensors

ABSTRACT

The present invention provides a system and method for multi-phase flow decomposition using electrical capacitance imaging techniques. The present invention provides a system and method to obtain permittivity distributions at a plurality of frequency markers using volume tomography image reconstruction to determine volume fraction of each phase and to produce images of the volume fraction for each phase.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.15/885,287, filed Jan. 31, 2018, which is a continuation of U.S.application Ser. No. 15/138,751, filed Apr. 26, 2016, which claimspriority to U.S. Provisional Application No. 62/153,095, filed on Apr.27, 2015. Each of which is incorporated by reference as if fully recitedherein.

BACKGROUND AND SUMMARY OF THE INVENTIVE FIELD

Multi-phase flow systems are the interaction between materials in whicheach has distinct and homogenous physical properties. Each component inthe flow that is homogenous in its physical properties and separable isreferred to as Phase. In a flow system, phase measurement is importantto properly optimize, control, and predict multiphase flow systems.Phase physical properties that are required to optimize of measure amultiphase process are phase distribution, velocity, and mass flow rate.It is desired to obtain such measurements for each phase individuallywhile all phases are interacting in a multiphase flow system. Forexample, for a multiphase flow system consisting of gas, liquid, andsolid particles, measured information of each individual phase is neededto properly control and understand the flow system.

Electrical capacitance sensors use the difference in dielectricconstants between phases to measure a capacitance signal. Thecapacitance signal is a measure of the effective dielectric constant forthe mixture of phases. From the measured effective dielectric constant,phase concentrations are inferred. This technique is most effective whenthe multiphase flow contains only two phases. For three or more phases,it is difficult to identify each phase concentration from a singlecapacitance measurement.

In the present invention, a method is devised to measure three or morephases in a multiphase flow system by exploiting theMaxwell-Wagner-Sillars (MWS) polarization effect, and using acapacitance sensor. The MWS effect is the change in effective dielectricof a mixture where at least one phase is conductive. Although each phasewould have a relatively fixed dielectric constant at frequencies in thequasi-static range, the mixture would have a frequency dependenteffective dielectric constant.

Typically, the transition in the frequency domain at which the effectivedielectric constant changes depends on the electric properties of theconductive phase that is causing this effect. For mixtures that havemultiple phases, multiple frequency transitions may occur where eachfrequency transition would be related to a phase in the mixture.Measuring capacitance at frequencies higher and lower relative to thetransition point provides a measurement that is specifically related tothe phase that caused this transition. In other words, a multiphase flowsystem can be decomposed to its individual phases where each phase ismeasured distinctly.

This multiphase decomposition approach can be extended to imaging ofeach phase distribution, distinctly, by using multiple capacitancesensors in formations that provide a tomography measurement. Here,Electrical Capacitance Tomography (ECT) is the reconstruction ofmaterial concentrations of dielectric physical properties in the imagingdomain by inversion of capacitance data from a capacitance sensor.

Electrical Capacitance Volume Tomography or ECVT is the direct 3Dreconstruction of volume concentration or physical properties in theimaging domain utilizing 3D features in the ECVT sensor design. ECVTtechnology is described in U.S. Pat. No. 8,614,707 to Warsito et al.which is hereby incorporated by reference.

Adaptive Electrical Capacitance Volume Tomography (AECVT) provideshigher resolution volume imaging of capacitance sensors based ondifferent levels of activation levels on sensor plate segments. AECVT isdescribed in U.S. Patent Application Publication US2013/0085365 A1 toMarashdeh et al. which is hereby incorporated by reference.

In ECT, ECVT, or AECVT, the capacitance measurement between sensorplates are also related to the effective dielectric content between thatplate pair. The phase's decomposition method can be extended to allmeasurements of ECT, ECVT, or AECVT sensors, thus providing a visualrepresentation of each phase, alone, through image reconstruction.

The relationship between effective dielectric constant and operatingfrequency is described in several empirical and theoretical approachesthat incorporate each phase volume fraction and electrical properties.As each phase electrical properties are known or can be measured, it isthe dynamic volume fraction distribution that is sought in multi-phaseflow imaging. Here, the instantaneous phase distribution and volumefraction is sought. Among the most notable formulations that relateeffective dielectric constant to each phase electric properties andvolume fraction are the Wiener, Bruggeman, and Wagner formulations.Those formulations, and all others, take the electric properties of eachphase and their volume fraction as inputs to estimate the effectivedielectric constant. The available different formulations are related tothe nature of the mixing between phases. For example, a system where allphases are homogenously mixed has a different formulation than a systemwhere phases are layered. Nevertheless, all formulations use the sameinputs to infer the effective dielectric constant. All effectivedielectric constant formulations can be summarized as:

ε_(effective) =f((∈′₁,σ₁,φ₁),(∈′₂,σ₂,φ₂) . . . (∈′_(n),σ_(n),φ_(a)),ω))

Where f is the formulation function, n is the number of phases in themulti-phase flow system, ω is the angular frequency at which capacitanceis being measured, and (∈′_(n), σ_(n), φ_(n)) are the complexpermittivity, conductivity, and volume fraction of the nth phase,respectively.

Using the effective permittivity formulation, capacitance sensors can beused to image each phase individually in this invention of multi-Phaseflow decomposition. As measured capacitance is linearly related to theeffective dielectric constant between capacitance plates used to measurecapacitance, developed formulation for effective dielectric constantscan be used to isolate each phase. Specifically, multiple capacitancemeasurements are taken at different frequencies. Capacitance acquiredusing an ECT, ECVT, or AECVT sensor at a single frequency is used toreconstruct an effective permittivity map. As capacitance is acquired atmultiple frequencies, a number of permittivity images equal to thenumber of frequencies will be available. Here, we assume each pixel inthe image is a well-mixed region of all phases in the multi-phase flow.The volume fraction of each phase in every pixel is calculated bysolving a number of equations equal to the number of phases. Thoseequations are obtained from formulations that related effectivedielectric constant at each frequency.

A data acquisition system operating at multiple frequencies is requiredfor phase decomposition. Capacitances can be measured at differentfrequencies successively or simultaneously. In the former approach, thedata acquisition speed of capacitance values at different frequenciesshould be higher than flow speed. In the latter, a synchronousdemodulator is used to isolate each capacitance value related to eachfrequency. Using both measuring schemes, the difference between measuredcapacitances (successive or simultaneous) is used to isolate the changein effective dielectric constant for multi-phase flow decomposition.

In the preferred embodiment, frequency transition points (markers) arefirst identified. As the effective dielectric constant changes as afunction of frequency, points at which there are sharp transitions inthe effective dielectric constant can be identified to calculate theeffective dielectric constant from a given frequency, volume fraction ofeach phase, and electrical properties of the mixture. For example, thiscan be accomplished by using the electrical properties of each singlephase alone, and then applying the MWS effect for the mixture based onthe volume fraction range for each phase in the mixture. Another methodof identifying the frequency transition points involves running a sweepfrequency signal of different frequency components and identifyingfrequency points where the effective dielectric constant of a mixtureundergoes a sharp transition. After the frequency points are identified,frequency markers are assigned. A frequency marker is an excitationsignal composed of one frequency above and below the identifiedtransition point. For multiple transition points, multiple markers canbe used. Each frequency marker measures the capacitance at a frequencyabove and below a transition point. The difference in measuredcapacitance at different frequency markers is related to the volumefraction of the phase that introduced this frequency transitionphenomenon in the effective dielectric value. As each phase hasdifferent electrical properties, the points at which each phasecontributes to a sharp transition in the effective dielectric constantof the whole mixture is distinct in the frequency domain, as is theidentification of frequency markers for each phase.

The measurements of capacitance difference for each phase marker areused to reconstruct 3D images of phase distribution in the imagingdomain. Following this approach, one can obtain more than one phasedistribution image, each corresponding to a different phase. The numberof different phase distribution images that can be obtained from thephase separation approach depends on the number of frequency transitionpoints and phase markers identified. Each single phase volume image canthen be used to reconstruct a global image where all phases are visible.

The need for a phase separation method is eminent in capacitancetomography. As capacitance measurements are related to the effectivedielectric constant between sensor plates, a maximum of two phases canbe imaged when capacitance measurements at a single frequency are used.Moreover, a number of physical properties can't be inferred directlyfrom the conventional capacitance imaging method. For example, thevelocity of each phase in a multiphase flow system varies based on thephysical properties of each phase. It is desirable to measure thevelocity of each phase to better control and understand the processesbeing measured. Capacitance based imaging provides a velocitymeasurement of the mixture, but not of each phase alone. Forapplications that involve mass flow gauging (i.e. oil logging andtransportation in pipelines or solids/liquid mass flow rates influidized beds) or those requiring a distinction between velocities ofdifferent phases, conventional capacitance sensors fall short. The phaseseparation method developed here fills the gap by providing a method ofimaging and measuring each phase independently, fulfilling a practicalneed for phase separation of multi-phase flow. Other applications thatcan utilize this technology are multiphase processes that use catalystsand imaging of the human body. Both of those examples involve phasesthat are conductive, thus enabling this phase separation approach.However, in cases where different layers are layered rather than mixed,the disclosed approach may be used to identify boundaries betweenphases. For example, applications that involve the human body wheretissues of different properties are layered, the disclosed invention canbe used to isolate each layer of similar tissues based on identifyingits boundaries.

The present invention provides an innovative ECVT sensor and supportingfeatures for multi-phase flow decomposition based on multi-frequencyapplication. This decomposition utilizes ECT, ECVT, or AECVT sensorswith a data acquisition unit that can measure capacitances at differentfrequencies. In the preferred arrangement, a signal of multiplefrequencies is sent to the sensing plate. The receiving plate employsseveral synchronous demodulations in parallel to measure the current atthe receiving plate at each frequency. The phase decomposition method isthen employed to extract information and generate volume images of eachphase individually. The frequencies that correspond to a specific phaseare identified based on electric properties of that phase, and othermixing phases in the multiphase flow system. As each phase has differentelectrical properties, the points at which each phase contributes to asharp transition in the effective dielectric constant of the wholemixture is distinct in the frequency domain, as is the identification offrequency markers for each phase.

The present invention also provides a method for identifying boundariesbetween different phases in the layered structure. For example, thehuman body is formed from different layers (skin, fat, bone etc.) thatare layered from the outside inward. As different layers have differentelectrical properties (dielectric constant and conductivity), the MWSeffect will take place at the interface between said layers. The phasedecomposition method can be used to identify boundaries between layersfor better imaging. Those boundaries can also be integrated in a globalvolume image where all phases are viewed simultaneously. The integrativeand adaptive data acquisition method is used to activate the ECVT sensorplates with different frequencies for detection and volumeidentification of rusted steel or broken steel cable strands.

An Adaptive data acquisition system can be extended to a new formationthat enables simultaneous capacitance measurement of capacitance atdifferent frequencies, as depicted in FIG. 3. Technical features of thesystem reported in PCT/US14/24457 can also be applied to the currentformation of block diagrams in the new formation reported in thispattern.

In (Ser. No. 14/564,204), a dual frequency approach was devised to imagesteel rust in tendons. The present invention is different in thefollowing ways: 1) it employs more than two frequencies to detectmultiple phases in the flow (in prior technology only a single phase wasaddressed); 2) it devises a method to establish frequency markers basedon knowledge of electrical properties for different phases; 3) a methodis also devised to quantify phases based on MWS effect; 4) imagereconstruction:

a—Capacitance is measured at all frequency markers for all combinationsof plate formations;b—An image is reconstructed using any available reconstruction(algebraic or optimization) technique for each set of capacitancemeasurements corresponding to a specific frequency;c—Each pixel or voxel (volume pixel) corresponding to the same locationin all reconstructed images is considered for phase decomposition inthat voxel. Here, the effective dielectric constant reconstructed ateach image will change based on the frequency used to measure thecapacitance and generate the image;d—The difference between effective dielectric constant in voxels locatedin the same location of each reconstructed image (across all images) isused to identify each phase volume fraction. Here, the effectivedielectric constant for a well-mixed multiphase flow system isformulated by relating the effective dielectric constant to the electricproperties of phases, the frequency used to measure capacitance, and thevolume fraction of each phase. Since all involved parameters are knownexpect for each phase volume fraction, a number of equations is formedfor each voxel location. The number of those equations is equal to thenumber of frequency points at which measurements were conducted. The setof equations is then solved to calculate the volume fraction of eachphase for every voxel (this will allow quantification of the percentageof volume occupied by each phase in the voxel);e—The process in d is repeated for each voxel location across all imagesreconstructed for capacitance measurements at different frequencies.Here, volume fraction of each phase is calculated at each voxellocation, combining the volume fraction of a single phase in all voxellocations provides a volume image of that phase alone;f—This phase decomposition process starts with a set of imagesreconstructed at different frequencies and ends at the same number ofimages, but each one corresponding to a single phase only. Individualphase volume fractions for each pixel (voxel) are combined together toform an image of that single phase alone. See steps above.

BRIEF DESCRIPTION OF THE DRAWINGS

The following detailed description of the example embodiments refers tothe accompanying figures that form a part thereof. The detaileddescription provides explanations by way of exemplary embodiments. It isto be understood that other embodiments may be used having mechanicaland electrical changes that incorporate the scope of the presentinvention without departing from the spirit of the invention.

In addition to the features mentioned above, other aspects of thepresent invention will be readily apparent from the followingdescriptions of the drawings and exemplary embodiments, wherein likereference numerals across the several views refer to identical orequivalent features, and wherein:

FIG. 1A illustrates one embodiment of three phases each having differentelectrical properties, in a background of a continuous phase.

FIG. 1B illustrates one embodiment of the sensor of the presentinvention.

FIG. 2 illustrates the embodiment of the sensor of FIG. 1B with themulti-phase flow components inside.

FIG. 3 illustrates one embodiment of the data acquisition design formeasuring capacitance at various frequencies, simultaneously.

FIG. 4 illustrates one embodiment of the multiphase structure organizedin a layered formation.

FIG. 5 illustrates one embodiment of frequency markers established for athree phase system, with two phases having electrical conductivity.

FIG. 6 illustrates one embodiment of an image with multiple voxels. Thisfigure shows how a volume in an image is digitized in small cells orvoxels. Applying phase decomposition method entails considering eachvoxel as a well-mixed cell where each phase is distributed homogeneouslyacross the voxel according to its volume fraction.

FIG. 7 a flow chart that explains the process of multiphase flowdecomposition.

FIG. 8 is a flow chart describing an example process of finding volumefraction distribution of three phases for image volume fractionconstruction.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENT(S)

FIG. 1A illustrates one embodiment of three phases (1,2,3) each havingdifferent electrical properties, in a background of a continuous phase(4). FIG. 1B illustrates one embodiment of the sensor of the presentinvention. In one embodiment, the sensor is comprised of 24 plates. Eachphase component will affect the effective dielectric constant of themixture and introduce a frequency dependent response based on theelectrical properties of the phases and the background.

FIG. 2 illustrates the embodiment of the sensor of FIG. 1B with thephases inside. As the flow evolves, the multi-phase components moveinside the sensor. Capacitance measurements between different platecombinations will also change in response to multiphase flow motion. Aphase in the multiphase flow will also cause the capacitance to changeas a function of frequency. This change is related to that phaseconcentration, volume fraction, and electrical properties.

FIG. 3 illustrates one embodiment a circuit diagram of the presentinvention. In this configuration, one receiver channel is used withmultiple synchronous demodulation paths, each for a specific frequency.The outputs of this circuit are capacitance values acquired at the sametime, and at different frequencies.

FIG. 4 illustrates one embodiment of a layered structure, with eachlayer having different electrical properties (dielectric constant andconductivity). In this structure, the interface between layers willreact differently to various frequencies. The result is a capacitancesignal that will change as a function of frequency. Knowing theelectrical properties of the structure, the MWS effect happens at theinterface between materials of different electrical properties. Forlayered materials, this effect would happen only at the interfacebetween layers. The different in capacitance measurements in this casecorresponds to the interfaces at which the effective dielectric constantchanges with frequency. Such ability would be of use for applicationsthat employ layered structures, like medical applications.

FIG. 4 illustrates the multiphase flow decomposition approach inidentifying and imaging boundaries between materials with differentelectrical properties as the MWS effect also takes place on theboundaries of such materials. Here, 5 and 7 are materials with differentelectrical properties (Dielectric constant and conductivity) and 6 is athird material of also different electrical properties sandwichedbetween 5 and 7. Here also, 8 and 9 are the boundaries between the threelayers where the response of the capacitance sensor changes as functionof applied frequency. The boundary regions will respond to frequencyeven if the capacitance for each layer alone (5, 6, and 7) is staticwith respect to frequency. In this arrangement, the frequency markersapproach can be used to identify and image boundaries between layeredmaterials of different properties.

FIG. 5 illustrates a typical chart of dielectric response of amultiphase flow mixture to frequency. The points at which the effectivedielectric constant of the mixture change are related to the electricalproperties of each phase in the multiphase flow mixture. From observingthe change in effective dielectric constant by measuring the frequency,the volume of each phase can be inferred. Conducting such measurementsusing an ECVT sensor would enable the imaging of each phaseindependently. This figure also shows the identification of frequencymarkers (f1 shown at 10). A frequency marker is a one that precedes orfollows a region of drastic change in the effective dielectric constantof a mixture. By plotting the effective dielectric constant as functionof frequency, sharp transitions can be observed. The number of sharptransitions is dependent on the number of phases involved, as depictedin this figure. A capacitance measurement is conducted between twotransitions, those points referred to as frequency markers. Acquiringcapacitance measurements at such markers provides capacitance data thatcan be used to image each phase in the multiphase flow independently.

FIG. 6 illustrates a typical digitization of an image with each cellrepresenting a voxel. Each voxel in the multi-phase flow decompositionapproach is assumed to be well mixed. “Well mixed” means each phase ishomogenously distributed in that voxel, according to its volumefraction. For example, if two phase are in a voxel, one has 0.3 volumefraction and the other is 0.7, the first phase is equally distributed inthe voxel such that it occupies 30% of the volume of the voxel. Thesecond phase is also equally distributed in the voxel such that itoccupies 70% of the voxel volume. In other words, each phase exists inevery part of the voxel, with its concentration depending on its volumefraction. The volume fraction of each phase is solved, in each voxel.Voxels are then combined with volume fractions of each phase, generatingmultiple images each for a single phase.

FIG. 7 illustrates a flow chart that describes the steps of implementingthe multi-phase flow decomposition approach for one embodiment of theinvention. The steps are preferably comprised of calibration,measurement, reconstruction, volume fraction solving, and phasedecomposition.

FIG. 8 illustrates an example flow chart describing the steps ofobtaining the volume fraction distribution of three phases using twofrequency ECVT measurements at two markers. For imaging N phases, N−1frequency measurements are required.

While certain embodiments of the present invention are described indetail above, the scope of the invention is not to be considered limitedby such disclosure, and modifications are possible without departingfrom the spirit of the invention as evidenced by the following claims.

1-20. (canceled)
 21. A system for generating a three-dimensionaltomograph of a vessel interior or other object and for multi-phase flowdecomposition, the system comprising: a capacitance sensor devicecomprising a plurality of electrodes for placement around the vessel orthe object, wherein the capacitance sensor device is adapted to provideelectric field distribution and sensor sensitivity in three geometricdimensions; data acquisition circuit in communication with thecapacitance sensor device for receiving input data from thethree-dimensional capacitance sensor device, the data acquisitioncircuit adapted to output electric phase signals at differentfrequencies; a hardware processing system in communication with the dataacquisition circuit, the hardware processing system programmed withinstructions for executing on the hardware processing system to: 1)measure electric phase shift in degrees or radians between an inputsignal to the sensor device and the current produced at an output of thesensor device at all of the different frequencies; 2) reconstruct athree-dimensional volume image from the electric phase shift measured atall of the different frequencies.
 22. The system for generating athree-dimensional tomograph of a vessel interior or other object and formulti-phase flow decomposition according to claim 21, wherein thehardware processing system is programmed with instructions for executingon the hardware processing system to reconstruct volume images of eachphase alone.
 23. The system for generating a three-dimensional tomographof a vessel interior or other object and for multi-phase flowdecomposition according to claim 22, wherein a reconstructed image basedon the electric phase difference is directly related to the phase. 24.The system for generating a three-dimensional tomograph of a vesselinterior or other object and for multi-phase flow decompositionaccording to claim 21, wherein the hardware processing system isprogrammed with instructions for executing on the hardware processingsystem to reconstruct images of the real or imaginary components ofeffective dielectric constant at each frequency.
 25. The system forgenerating a three-dimensional tomograph of a vessel interior or otherobject and for multi-phase flow decomposition according to claim 21,wherein the hardware processing system is programmed with instructionsfor executing on the hardware processing system to reconstruct aplurality of images, each with a single-phase volume fraction image. 26.The system for generating a three-dimensional tomograph of a vesselinterior or other object and for multi-phase flow decompositionaccording to claim 21, wherein the hardware processing system isprogrammed with instructions for executing on the hardware processingsystem to obtain volume fractions of each phase for each voxel.
 27. Thesystem for generating a three-dimensional tomograph of a vessel interioror other object and for multi-phase flow decomposition according toclaim 26, wherein the hardware processing system is programmed withinstructions for executing on the hardware processing system to combinepixels for a single phase volume fraction to formulate an image for thephase.
 28. The system for generating a three-dimensional tomograph of avessel interior or other object and for multi-phase flow decompositionaccording to claim 21, wherein the data acquisition circuit is adaptedto output capacitance signals for each of the different frequencieswherein the hardware processing system is programmed with instructionsfor using the output capacitance or electric phase signals for each ofthe different frequencies to reconstruct the three-dimensional volumeimage.
 29. The system for generating a three-dimensional tomograph of avessel interior or other object and for multi-phase flow decompositionaccording to claim 28, wherein the hardware processing system isprogrammed with instructions for generating volume images of each phaseof the multi-phase flow individually.
 30. A system for generating athree-dimensional tomograph of a vessel interior or other object and formulti-phase flow decomposition, the system comprising: a capacitancesensor device comprising a plurality of electrodes for placement aroundthe vessel or the object, wherein the capacitance sensor device; dataacquisition circuit in communication with the capacitance sensor devicefor receiving input data from the three-dimensional capacitance sensordevice, the data acquisition circuit adapted to output capacitancesignals and electric phase signals at different frequencies; a hardwareprocessing system in communication with the data acquisition circuit,the hardware processing system programmed with instructions forexecuting on the hardware processing system to: 1) measure electricphase shift in degrees or radians between an input signal to the sensordevice and the current produced at an output of the sensor device at allof the different frequencies; 2) reconstruct a three-dimensional volumeimage from the electric phase shift measured at all of the differentfrequencies.
 31. The system for generating a three-dimensional tomographof a vessel interior or other object and for multi-phase flowdecomposition according to claim 30, wherein the hardware processingsystem is programmed with instructions for executing on the hardwareprocessing system to reconstruct volume images of each phase alone. 32.The system for generating a three-dimensional tomograph of a vesselinterior or other object and for multi-phase flow decompositionaccording to claim 31, wherein a reconstructed image based on theelectric phase difference is directly related to the phase.
 33. Thesystem for generating a three-dimensional tomograph of a vessel interioror other object and for multi-phase flow decomposition according toclaim 30, wherein the hardware processing system is programmed withinstructions for executing on the hardware processing system toreconstruct images of the real or imaginary components of effectivedielectric constant at each frequency.
 34. The system for generating athree-dimensional tomograph of a vessel interior or other object and formulti-phase flow decomposition according to claim 30, wherein thehardware processing system is programmed with instructions forgenerating volume images of each phase of the multi-phase flowindividually.
 35. The system for generating a three-dimensionaltomograph of a vessel interior or other object and for multi-phase flowdecomposition according to claim 30, wherein the hardware processingsystem is programmed with instructions for using the capacitance andelectric phase signals at different frequencies to measure a volumefraction of each phase of the flow and for using each capacitance orelectrical phase signal to calculate the velocity for each phase of theflow.
 36. The system for generating a three-dimensional tomograph of avessel interior or other object and for multi-phase flow decompositionaccording to claim 35, wherein the hardware processing system isprogrammed with instructions for using the product of velocity andvolume fraction for each phase of the flow to determine mass flow rate.37. A system for generating a three-dimensional tomograph of a vesselinterior or other object and for multi-phase flow decomposition, thesystem comprising: a capacitance sensor device comprising a plurality ofelectrodes for placement around the vessel or the object; dataacquisition circuit in communication with the capacitance sensor devicefor receiving input data from the three-dimensional capacitance sensordevice, the data acquisition circuit adapted to output capacitancesignals and electric phase signals at different frequencies; a hardwareprocessing system in communication with the data acquisition circuit,the hardware processing system programmed with instructions forexecuting on the hardware processing system to: use the capacitance andelectric phase signals at different frequencies to measure a volumefraction of each phase of the flow and for using each capacitance orelectrical phase signal to calculate the velocity for each phase of theflow.
 38. The system for generating a three-dimensional tomograph of avessel interior or other object and for multi-phase flow decompositionaccording to claim 37, wherein the hardware processing system isprogrammed with instructions for using the product of velocity andvolume fraction for each phase of the flow to determine mass flow rate.